soln Algorithm
The Soln Algorithm is an innovative approach to solving complex optimization problems, particularly in the field of operations research, artificial intelligence, and machine learning. It is based on the principles of natural evolution, which involve the processes of selection, crossover, and mutation. The algorithm simulates the evolution of a population of candidate solutions over time, with the fittest individuals being more likely to survive and reproduce. By mimicking these natural processes, the Soln Algorithm can efficiently explore the solution space and converge towards an optimal or near-optimal solution. It is a versatile and adaptive technique that can be applied to a wide range of optimization problems, from scheduling and routing to game playing and function optimization.
The Soln Algorithm starts with an initial population of randomly generated candidate solutions, each representing a possible answer to the given optimization problem. Through an iterative process, the algorithm evaluates the fitness of each individual in the population, selecting the best ones to participate in the reproduction process. This is typically achieved through a selection method, such as tournament selection or roulette wheel selection, which favors fitter individuals. Once the parents are selected, the algorithm performs crossover and mutation operations to generate new offspring, combining and modifying the genetic material of the parents. This process introduces diversity and innovation into the population, allowing the algorithm to explore new regions of the solution space. After the new generation is formed, the algorithm repeats the process of evaluating, selecting, and reproducing individuals until a predefined stopping criterion is met, such as a maximum number of generations or a satisfactory fitness level. The best individual found during the search process is then returned as the optimal or near-optimal solution to the problem.
""" Problem Statement (Digit Fifth Power ): https://projecteuler.net/problem=30
Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
1634 = 1^4 + 6^4 + 3^4 + 4^4
8208 = 8^4 + 2^4 + 0^4 + 8^4
9474 = 9^4 + 4^4 + 7^4 + 4^4
As 1 = 1^4 is not a sum it is not included.
The sum of these numbers is 1634 + 8208 + 9474 = 19316.
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
(9^5)=59,049
59049*7=4,13,343 (which is only 6 digit number )
So, number greater than 9,99,999 are rejected
and also 59049*3=1,77,147 (which exceeds the criteria of number being 3 digit)
So, n>999
and hence a bound between (1000,1000000)
"""
def digitsum(s: str) -> int:
"""
>>> all(digitsum(str(i)) == (1 if i == 1 else 0) for i in range(100))
True
"""
i = sum(pow(int(c), 5) for c in s)
return i if i == int(s) else 0
if __name__ == "__main__":
count = sum(digitsum(str(i)) for i in range(1000, 1000000))
print(count) # --> 443839
